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Solar Energy 97 (2013) 356–368

High temperature solar thermal central-receiver billboard design

Nicholas Boerema a,⇑, Graham Morrison a, Robert Taylor a, Gary Rosengarten a,b

a School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW 2052, Australiab School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Melbourne, Vic 3001, Australia

Received 28 January 2013; received in revised form 19 August 2013; accepted 3 September 2013Available online 24 September 2013

Communicated by: Associate Editor Ranga Pitchumani

Abstract

The design of central receivers in solar thermal power plants is critical for efficient plant operation and sufficient operational lifetimes.The high, non-uniform concentration ratios used in central receivers lead to high, non-uniform receiver temperatures. For the same oper-ational conditions, small changes to the receiver design can make a big impact on the expected lifetime of the receiver. This is due tolimitations of the receiver materials to high temperatures and thermal cycling. In this study, we investigate the effect of several engineer-ing concepts on the resultant surface temperatures of tubular billboard receivers. Four tubular billboard designs are investigated alongwith the sensitivity these designs have to high temperatures resulting from changes in the aiming point of the heliostat array. We exam-ined a receiver with single diameter tubes, an ideal flow receiver, a receiver using various diameter tubes and a receiver made of tubepanels in series. The single-diameter and multi-diameter receivers were found to have high temperatures and high sensitivity undernon-standard irradiation. The multi-pass receiver was found to out-perform the other designs by reducing both the maximum surfacetemperatures under standard irradiance and the risk of high temperatures from irradiance changes. The results provide insights intotubular billboard receiver design, material selection and design for extended life.� 2013 Elsevier Ltd. All rights reserved.

Keywords: Concentrated solar thermal; Central receiver system; Receiver design; Billboard

1. Introduction

Solar thermal Central Receiver Systems (CRSs) areexpected to provide a path for achieving large-scale deploy-ment of electricity generators that use a renewable resource(IEA, 2010). CRSs consist of a field of heliostats whichfocus solar radiation towards a receiver, situated at thetop of a tower. Solar energy is collected in the receiverusing a heat transfer fluid (HTF) which is then used totransfer the energy to a thermodynamic cycle (via steam)to allow electricity generation. CRSs may consist of a large,single tower design (such as used at Gemasolar (Dunnet al., 2012)), or multiple towers may be used, such as inthe eSolar design (Schell, 2011).

0038-092X/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.solener.2013.09.008

⇑ Corresponding author. Tel.: +61 428828015.E-mail address: nicholas.boerema@student.unsw.edu.au (N. Boere-

ma).

Focusing the reflected light from the heliostats towardsa point means that high solar concentration ratios can beachieved on the receiver. High concentration ratios meanhigh receiver efficiencies, and allow higher working cycletemperatures to be achieved which leads to higher thermo-dynamic efficiencies. Increasing the efficiency is importantfor CRSs, as it reduces the required size of the heliostatfield for the same generation capacity. This is crucial toeconomic viability since the heliostat field makes upapproximately 40% of the systems capital costs (Hinkleyet al., 2011). To further increase efficiency, small receiverareas are desired as this reduces receiver losses from con-vection and re-radiation (Bignon, 1980). A challenge forCRSs is to increase the durability of the highly irradiatedreceiver, whilst allowing high temperatures to be achievedand ensuring a cost effective design.

Whilst cavity and volumetric receivers are receiving a lotof attention from the academic community (Romero et al.,

Nomenclature

Acronyms

CRS central receiver systemHTF heat transfer fluidDNI direct normal irradiance

Symbols

Nu Nusselt numberRe Reynold’s numberPr Prandtl numberT1 HTF temperature at start of stepT2 HTF temperature at end of step_Qf heat transfer to segment of HTF (W)_m mass flow rate (kg/s)Cp HTF specific heat at constant pressure (J/kg K)

hcombined enthalpy of the combined HTF from all recei-ver pipes in parallel (J/kg)

_mcombined combined HTF from all receiver pipes in par-allel (kg/s)

hk enthalpy of HTF at exit of kth receiver pipe (J/kg)

_mk mass flow rate of kth receiver pipe (kg/s)DP pressure drop (Pa)f friction factorL receiver pipe length (m)D receiver pipe internal diameter (m)q density (kg/m3)V velocity (m/s)

N. Boerema et al. / Solar Energy 97 (2013) 356–368 357

2002; Avila-Marın, 2011), it is external tubular receiversthat are being used most in commercial central receiverprojects (NREL, 2011; IT Power, 2012). This results fromtubular receiver technology being built on concepts fromheat exchanger design – i.e. relatively inexpensive, durable,proven technology.

Currently, the majority of commercial systems beingdeployed are using a surround tower heliostat field whichfocus incident light onto a cylindrical tubular receiver.Modelling of heliostat layouts has shown that equator fac-ing heliostat fields can greatly increase the field optical effi-ciency, which reduces the size of the heliostat field requiredcompared to a surround tower design (Collado, 2009;Schell, 2011). Equator facing fields have a lower mirror areato number of towers ratio, which means that they are moresuited to a plant design that uses multiple smaller towers.

A result of multiple smaller towers is that the cost of thereceiver becomes more critical due to the number required.The importance of simple operation is also increased for thesame reasons. For an equator facing heliostat field a cylin-drical receiver is no longer a suitable design. Instead, a suit-able option is a billboard receiver, which consists of a groupof vertical tubes, aligned in a single plane (Eduardo andManuel, 2007). This receiver design and field layout, how-ever, can result in highly non-uniform flux densities, whichcan introduce high surface temperatures. As the thermalstresses are related to the surface temperatures, it is neces-sary to predict and control these temperatures.

Tracking error is inherent in all heliostats, due to sunpositioning error, referencing errors, gravity sag, pedestaltilt, mirror and support vibration (wind impacts), cant-ing/bore sight errors and gear backlash. These errors canbe reduced, but in general this incurs an increase in helio-stat and system costs (Zhang et al., 2012). This error leadsto a probability distribution of where the reflected light willland on the receiver for a given aiming point. Due to thisdistribution it is undesirable to focus the heliostats towardsthe edges of a billboard receiver as this increases spillage

(where incident irradiance misses the receiver). This cancause issues for billboard receivers as the incident irradi-ance is highly concentrated towards the centre of the recei-ver. This non-uniform flux distribution can lead to veryhigh surface temperatures. As the thermal stresses arerelated to the surface temperatures, it is necessary to pre-dict and control the receiver surface temperatures. If tem-peratures are known, receiver materials and design can beselected appropriately to handle the stresses over its20,000–100,000 h design operational life.

In selecting a material for the receiver tubes, this highnumber of thermal cycles must be considered. The numberof thermal cycles needed to be withstood over the tube life-time is environment specific but will be in the tens to hun-dreds of thousands. This thermal cycling means that theissues encountered in conventional heat exchanger designswill be exacerbated for the same maximum temperaturelimits of operation. Furthermore the non-isothermal condi-tions across the receiver mean that multiple temperatureregions must be considered. Significant issues to considerare loss in ductility and tensile strength, creep and carburi-zation rates, fatigue crack growth rates, and oxidationresistance. Fig. 1a demonstrates a loss in material strengthresulting from high service temperatures whilst Fig. 1bshows the clear trend in increasing crack growth rate withincreasing temperature. Together, the figures demonstratethe need to understand the expected temperatures thatare likely to result for a given receiver design.

To assist in this understanding, an assessment of theresultant surface temperatures has been performed for fourdifferent billboard designs; a multi-pass receiver, asingle-diameter receiver, an ideal flow receiver, and amulti-diameter receiver.

1.1. Receiver concepts

The single-diameter billboard design (Fig. 2) is the sim-plest of the designs as it uses only a single panel made of

(a) (b)

Fig. 1. (a) Creep rate curves for several austenitic stainless steels: 1% creep in 100,000 h (Davis, 2001). (b) Variation of fatigue crack growth rate as afunction of temperature at stress intensity factor = 30 MPa

ffiffiffiffimp

(Viswanathan, 1989). Da/dN indicates the increase in crack length for each cycle N, ofsinusoidally varying applied stress.

Fig. 2. Schematic of conventional single pass tubular billboard receiver.

358 N. Boerema et al. / Solar Energy 97 (2013) 356–368

uniform diameter, parallel pipes. This design operates witha uniform flow rate through each pipe. Thus, for a non-uni-form irradiance profile, the exit temperature of the HTF inthe central pipes is much higher than the outer tubes toallow a sufficiently high mean temperature after all the fluidmixes. As the surface temperature of the receiver will beabove the HTF temperature, high surface temperatures willresult. This places the receiver under thermal strains whichstandard stainless alloys may not be able to handle for thelength of the receiver’s design life (Ward, 2012). To mini-mise receiver costs it is desirable to be able to use low-coststainless steels, and thus methods for reducing the maxi-mum temperature of this receiver design need to bedeveloped.

One way to reduce surface temperatures is to ensure thatthe HTF from all pipes reaches the desired outlet tempera-ture. This could be achieved by either using flow controldevices or through varying the pipe geometry to matchthe heat flux on each pipe. An “ideal flow receiver” isproposed here (Fig. 3a), in which the flow rate of each

individual tube is adjusted such that the fluid outlet tem-perature for each tube is equal to the desired exit tempera-ture for any flux distribution.

A multi-diameter receiver is proposed (Fig. 3b) to par-tially achieve this. This receiver uses a selection of multiplediameter pipes-each with a single diameter – to make upthe receiver. As the pipes are in parallel the pressure dropalong each pipe will be equal. The mass flow rate is thenproportional to the pipe flow resistance only. As the pres-sure drop is constant between pipes, the smaller diameterpipes have a higher resistance to flow and thus a lowermass flow rate which will heat up more easily. Thus, fora Gaussian flux distribution; by using smaller diameterpipes towards the edge of the receiver, where irradiance islower, outlet temperatures closer to that desired can beachieved.

The multi-pass tubular billboard design (Fig. 3c) ismade up of multiple side-by-side panels through whichthe HTF passes in both series and parallel, beginning inthe outer panels and finishing by passing through the centremost panel (Schiel and Geyer, 1988). The HTF may becombined in a header between panels. As the irradianceis greatest towards the centre, this design allows the HTFtemperature to be better matched to the irradiance level.The main issue with this receiver design is that it is not pos-sible to completely drain the receiver of the HTF withoutusing additional valves. This leads to undesirable complex-ity and additional costs. Whilst it is beyond the scope ofthis paper, multiple diameters could also be incorporatedinto this design.

2. Model development

To determine the surface temperatures that will resultfrom a given receiver flux distribution, a heat transfermodel of a tubular billboard receiver has been developed.For the model, the flux distribution, the inlet temperatureand desired outlet temperature are used as inputs. As out-puts, the necessary flow rate and resultant heat transfer andsurface temperatures are solved. The model allows forcomparison between single-diameter, multi-diameter andmulti-pass receivers.

Fig. 3. (a) Ideal flow receiver. (b) Multi-diameter receiver. (c) Multi-Pass receiver.

Fig. 4. Flux distribution (red) about the tube perimeter. (For interpreta-tion of the references to colour in this figure legend, the reader is referredto the web version of this article.)

N. Boerema et al. / Solar Energy 97 (2013) 356–368 359

For the receiver model, sodium has been taken as theheat transfer fluid, using equations for the thermophysicalproperties and pressure drop as described by Fink andLeibowitz (1995) and Boerema et al. (2012). The followingequation for calculating the Nusselt number in turbulentflow has been used and is recommended by Cengel (2007)for liquid metals due to their very low Prandtl numbers.

Nu ¼ 6:3þ 0:0167Re0:85Pr0:93s ð1Þ

where Re is the Reynold’s number and Prs is the Prandtlnumber calculated using properties at the pipe inner sur-face temperature. For Eq. (1) the flow is assumed to be tur-bulent and fully developed. The assumption of turbulencewas seen as valid due to Reynold’s numbers calculatedbeing on the order of 104. The assumption of fully devel-oped flow was seen as valid as normally a tubular receiverwill have some unexposed tube before the irradiated sec-tion, which would provide sufficient length for the flow tobecome fully developed.

Sodium has been used as the heat transfer coefficient dueto its high thermal conductivity which makes the resultantheat transfer coefficients less dependent on the flow condi-tions. Other heat transfer fluids would have similar surfacetemperature distributions for a given receiver concept,however the tube lengths would need to be adjusted toensure that adequate flow rates were achieved to insure suf-ficient heat transfer. Surface fouling has been assumed tobe negligible.

2.1. Receiver flux distribution

The flux distribution on the target depends on the par-ticular heliostat design, the field layout and the time ofday. In this study a heliostat field with a single point aiming

strategy has been used. The resulting flux distributionacross the receiver aperture has been approximated by anormal (Gaussian) distribution, with a mean located atthe centre of the receiver. The standard deviation of the dis-tribution will depend namely on the referencing errors,gravity sag, pedestal tilt and canting/bore sight errors,the amount of backlash in the gears, mirror errors andenvironmental conditions (wind). The flux will be distrib-uted about the exposed section of the perimeter for eachof the receiver pipes. For the exposed section, taken as180� of pipe for this study, the distribution about theperimeter is approximately given by q(h) = qnet�cos (h),where qnet is the intensity of the incident radiation (seeFig. 4) (Yang et al., 2012).

A 1.5 m � 1.5 m receiver made up of parallel tubes hasbeen used. For the flux distribution, a mean of zero and

Fig. 5. Flux distribution across the receiver aperture. Mean = 0, standard deviation = 0.255�Width.

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a standard deviation of 0.255�Width has been chosen,resulting in approximately 10% spillage and leading to anaverage incident irradiance of 737 kW/m2 across the recei-ver aperture. To create the distribution (Fig. 5), the receiveraperture was first divided into a mesh, with an integer num-ber of segments per receiver tube. The spillage fraction inthe vertical and horizontal directions was then decidedand used respectively to calculate the standard deviationfor the flux distributions for the two directions. A lowerspillage fraction results in a lower standard deviation forthe flux distribution and thus a higher peak flux. Matlab’smultivariate normal cumulative distribution function wasthen used to calculate the multivariate normal cumulativeprobability evaluated over each segment. This gives theexpected percentage of incident energy landing on each seg-ment. This fraction was then multiplied with the totalenergy coming from the field to give the energy landingon each segment.

2.2. Heat transfer calculations

One-dimensional heat transfer calculations have beenperformed on the receiver by dividing each pipe into 10evenly spaced segments across its diameter and into seg-ments of length 50 mm along the pipes main axis. To startthe calculations, an initial mass flow rate is assumed. Usingthe fluid inlet temperature, the fluid properties and the fric-tion factor, the heat transfer coefficient can be calculatedfor the first segment. The pipe wall thermal resistance,the thermal convective resistance and the total resistancecan be calculated using standard one dimensional pipethermal resistance equations (Cengel, 2007, pp.146–152).

The segment’s surface temperature can then be solvedby simultaneously solving standard heat transfer equationsfor conduction/convection to the HTF and radiative andconvective heat losses to the surroundings, such that thecombined energy transferred is equal to the absorbedenergy. This also solves the energy transferred to theHTF for each segment and the thermal losses of each

segment. The energy transferred to the HTF for each seg-ment of a single step along the pipes main axes can thenbe summed together to give the total energy transferredto the HTF for that step, _Qf .

The convective heat transfer coefficient is dependent onenvironmental conditions and as such a reference value of16 W/m2 K has been used. This relates to a wind speed ofapproximately 4 m/s (Kesselring and Selvage, 1986, pp.5.7–24). For simplicity, the view factor between the pipesand the surrounds has been approximated as cosh. Areflectivity of 0.08 has been used for the Pyromark surfacecoating. This value has been adjusted by a correction factorof 0.72 to account for the reflectivity of light off of the pipesonto other pipes, giving a corrected reflectivity of 0.0576(thus absorptivity = 0.9424). The correction factor wasapproximated from calculations made for this geometryby Kesselring and Selvage (1986, pp. 5.1–9).

Assuming sufficient mixing, the sum of the heat transferto the HTF, _Qf , for all segments in a single step along thepipes main axis, can then be used to calculate the temper-ature at the end of the step (T2) and is given by:

T 2 ¼_Qf

_mCpþ T 1 ð2Þ

T1 is the temperature at the start of the step and is equal tothe inlet temperature for the first step. _m is the mass flowrate through a single pipe and Cp is the specific heat ofthe fluid, calculated as a function of temperature. Thesecalculations can be repeated for each pipe in the receiver.The exit temperature of the combined fluid leaving the re-ceiver pipes (i.e. the header temperature) can be solved forby using the enthalpy of the combined HTF:

hcombined ¼1

_mcombined

Xn

k¼1

_mkhk ðJ=kgÞ ð3Þ

where _mcombined is the combined mass flow rate and n is thetotal number of pipes. _mk and hk are the mass flow rate andenthalpy, respectively, for the kth pipe. The process can be

Fig. 6. Schematic representation of the flow path for the advanced sodiumreceiver at IEA–SSPS.

N. Boerema et al. / Solar Energy 97 (2013) 356–368 361

iterated, adjusting the mass flow rate until the exit temper-ature of the combined fluid leaving the receiver pipes isequal to the desired exit temperature. To match with com-mon tower operational conditions, a desired exit tempera-ture of 570 �C has been used (Kolb, 2011).

2.3. Validation and verification

To verify the model for the different receiver designs var-ious predictable tests were run and the results comparedwith those expected. These included a uniform flux distri-bution, and zero loss cases-where all incident energy isabsorbed and the thermal emissivity and coefficient of heattransfer were reduced to zero. The uniform flux distribu-tion meant that the surface temperatures were identicalfor each tube and increasing approximately linearly withfluid temperature.

Grid convergence studies were performed on the modelto ensure that an adequate mesh density has been chosen.Various predictable cases, such as uniform intensities andno losses were also performed to verify the model. For sim-plicity, conduction along and around the tubes wasneglected, as was absorption of reradiated light from neigh-bouring tubes. These heat transfer mechanisms would acttowards levelling temperatures across the receiver, how-ever, the energy transferred is minimal relative to theincoming flux, due to the low pipe-to-pipe view factorand low thermal conductivity and cross-sectional area ofthe tube.

The results of the model were validated through com-parisons with results from the IEA–SSPS sodium receiverand the thermodynamic model “HOTREC” developedand validated as part of the IEA–SSPS program (Schieland Geyer, 1988). The SSPS sodium receiver was a bill-board receiver which consisted of 5 panels each made upof 39 tubes of 14 mm diameter and 1 mm wall thickness.The sodium was passed through each of these panels in ser-ies. The order through which the panels were passed can beseen in Fig. 6. Results from testing of the receiver and fromthe thermodynamic model were presented by Schiel andGeyer (1988) for both a triple point aiming strategy anda single point aiming strategy. In the triple point aimingstrategy a third of the light from the heliostat field wasfocused onto each of the three central panels. In the singlepoint aiming strategy all incident light was focused ontothe central panel. HOTREC results presented were devel-oped using 2.76 MW and 2.8 MW for the incident powerin the triple and single aim points respectively. The peakflux for the triple aiming point strategy was 1.6 MW/m2,whilst for the single aiming point strategy the peak fluxwas 2.3 MW/m2. To allow validation of our model it wasattempted to match the flux and the peak fluxes used inthe IEA–SSPS project such that the HTF, pipe outer sur-face and Pyromark surface coating temperatures could becompared with those presented. In the vertical directionthe flux is presented for the central pipe. For the horizontaldirection the absorbed energy in each panel was presented

whilst panel efficiencies were presented by Kesselring andSelvage (1986). The absorbed energy, however, alsoincluded the effect of 30 broad focused heliostats, whichadded another 0.6 MW to the total power and 0.1 MW/m2 to the peak flux. These values were used to calculatethe fraction of incident energy on each panel for the HOT-REC model, which was then attempted to be achieved withour flux, whilst still maintaining the correct overall incidentenergy and peak flux. It should be noted that an exactmatch of the flux was not achievable due to the numberof variables and the limited information presented in theSchiel and Geyer paper and as such there is some misalign-ment with the temperatures and incident energy on eachpanel.

Figs. 7 and 8 allow a comparison between the HOTRECmodel and our model for the temperatures of the centraltube of the fifth panel for both the single aiming pointstrategy (Fig. 7) and the triple aiming point strategy(Fig. 8). Considering the flux mismatch, the temperatureresults show very good agreement. This agreement withthe grid convergence tests gave us confidence in the validityof our model.

Table 2 shows the percentage of incident energy for eachpanel, used to help create the flux profile, and the resultantefficiencies for each panel. Comparing the efficiencies forthe triple point aiming strategy they are also in good agree-ment, considering the flux mismatch and number ofparameters.

Fig. 7. Temperature and heat flux profiles along the central tube of the fifth panel as calculated by HOTREC and our model for the single point aimingstrategy with incident power = 2.8 MW and peak flux = 2.3 MW/m2.

Fig. 8. Temperature and heat flux profiles along the central tube of the fifth panel as calculated by HOTREC and our model for the triple point aimingstrategy with incident power = 2.76 MW and peak flux = 1.6 MW/m2.

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3. Receiver surface temperatures

To compare the different designs a consistent set ofreceiver variables have been used, as outlined in Table 1.

3.1. Centred flux distribution

3.1.1. Single-diameter receiver

The resultant surface irradiance and surface tempera-tures of a single-diameter billboard receiver has been deter-mined. Tubes with an outer diameter of 25.4 mm, a lengthof 1.5 m and a wall thickness of 1 mm have been used. The

flux distribution across the receiver tubes is presented inFig. 9. The thermal efficiency for this receiver under themodelled conditions is 91.2%, where receiver efficiency isdefined as energy absorbed by the HTF to energy incidenton the receiver (and thus does not include spillage).

Fig. 10 shows the resultant surface temperatures indicat-ing a maximum pipe surface temperature of 861 �C whentrying to achieve an outlet temperature of 570 �C. Thelow irradiance levels on the pipe surfaces towards the edgeof the receiver result in a low exit temperature for thosepipes. To compensate, the inner pipes must have a fluid exittemperature well above the desired operating temperature

Table 1Parameters used in the model.

Example parameters Value

Pipe thickness 1 mmPipe thermal conductivity 20 W/mKPipe thermal expansion coefficient 17.3 � 10�6

Pipe roughness 0.002 mmReceiver pipe length 1.5 mReceiver width 1.5 mReflectivity 0.08Corrected reflectivity 0.0576Emissivity 0.85Surface heat transfer coef. 16 W/m2 KInlet temperature 200 �CDesired outlet temperature 570 �CFlux standard deviation 0.389 mSpillage 10%Ambient temperature 20 �CTotal flux 1.68 MWAve. irradiance on Receiver 737 kW/m2

Fig. 9. Flux distribution across the receiver tube surfaces.

Fig. 10. Pipe surface temperatures to achieve a desired outlet temperatureof 570 �C.

N. Boerema et al. / Solar Energy 97 (2013) 356–368 363

(Fig. 11). As the surface temperature will be above the fluidtemperature, the result of this is high surface temperaturestowards the centre of the upper portion of the receiver.

An issue in this receiver design is that if the aiming pointfor all heliostats moves away from the centre of the recei-ver, very high surface temperatures will result if the flowrate is adjusted such that the desired operating temperatureis still achieved. To reduce this risk, control which ensuresminimum flow rates could be used. These flow rates couldbe based on the sun’s direct normal irradiance (DNI) leveland the number of heliostats focused on the receiver. Forgreater protection a camera would likely be needed,focused on the receiver. The images from the camera wouldthen allow imaging software to determine the mean of theirradiance distribution and the heliostat aiming could beadjusted accordingly as is done by BrightSource Energy(Bobinecz, 2012). Whilst these methods exist to limit hightemperature occurrences, the particular temperature stabil-ity of each receiver design under rapid irradiance fluctua-tions, and shifts in the focus point should be understoodso that the risks can be designed for accordingly.

Tubular receivers can also be used in a cavity, as a cavityreceiver. The aim of this is to reduce losses from convectionand re-radiation and to try and achieve an even flux inten-sity across the receiver surface. This is achieved through re-radiation inside the cavity and through the incident lightbeing reflected off of the cavity walls. For comparison with

Table 2Incident energy and efficiencies for each panel for validation.

Incident Energy

Single point aiming Triple point aiming

Hotrec (%) Ours (%) Hotrec (%) Ours (

Panel 1 2 3 4 4Panel 4 21 24 27 27Panel 5 49 45 33 36Panel 3 26 24 29 28Panel 2 2 3 6 5

the other receiver designs the uniform diameter receiver hasalso been modelled with an even flux distribution of737 kW/m2. The maximum surface temperature seen is632 �C and the resultant receiver efficiency is 91.8%. Dueto the even distribution of the light, the surface tempera-tures are the same for all pipes which will result in lowerthermal stresses.

Efficiency

Single point aiming Triple point aiming

%) Hotrec Ours (%) Hotrec (%) Ours (%)

N/A 78 84 81N/A 90 91 90N/A 90 90 89N/A 91 92 91N/A 78 84 81

Fig. 11. Difference between the HTF exit temperature and the desired exit temperature for a standard billboard receiver with a centred normal heat fluxdistribution with a mean irradiance of 737 kW/m2.

364 N. Boerema et al. / Solar Energy 97 (2013) 356–368

3.1.2. Ideal flow receiver

The energy balance for the ideal flow receiver can besolved as before, however, this time the mass flow rate isadjusted for each individual pipe until the exit temperatureis equal to the desired outlet temperature.

In Fig. 12 it can be seen that the maximum surface tem-perature has now been reduced to approximately 634 �C, areduction of over 200 �C. The efficiency achieved was91.6%. As each pipe now has a similar temperature distri-bution the thermal expansion of each pipe will also be sim-ilar. This will reduce the thermal strains on the receiver.Fig. 13 shows the mass flow rate of each pipe normalisedwith the flow rate of the centre pipe. For equal fluid exittemperatures the flow rates need to be reduced to this frac-tion. Methods to actively control individual flow rates maybe expensive, however, there may be cheaper passivetemperature actuated options.

Fig. 12. Pipe surface temperatures (�C) for a receiver using individuallyadjusted mass flow rates for each pipe.

3.1.3. Multi-diameter receiver

Flow control can be locked in using different pipe diam-eters at different parts of the receiver to control the flowresistance. Calculations for the multi-diameter receivermust solve for the mass flow rate of each pipe such thatthe pressure drop through all pipes is equal and the desiredheader temperature is achieved.

Using properties at the average fluid temperature, thepressure drop can be calculated using the Darcy–Weisbachequation, with the friction factor calculated using the expli-cit equation developed by Haaland (1983).

Taking one pipe as the reference pipe, the mass flowrates of the other pipes can be adjusted such that the pres-sure drop for each pipe is the same as the reference pipe.The flow rate of the reference must then be adjusted toensure that the exit temperature of the combined fluidremains equal to the desired exit temperature.

Fig. 14 shows receiver surface temperatures for a receiverusing 11 different pipe diameters (evenly spaced from 12 mmto 25.4 mm). As can be seen, the maximum surface temper-atures have been reduced (maximum temperature: 707 �C).The reduction in temperatures is, however, far from thatachieved with uniform outlet temperatures (634 �C). Theefficiency for this receiver under the stated conditions is92.6%. This efficiency is higher than the even flux receiveras the side tubes allow collection of the incident energy,whilst not needing to achieve the desired outlet temperatures(and thus they maintain a low surface temperature). Thelower than desired outlet temperatures can be easily bal-anced by the higher volume and more highly irradiated pipesnear the horizontal centre of the receiver. In effect, the recei-ver surface area with high temperatures is reduced withoutincreasing the maximum temperature significantly.

3.1.4. Multi-pass receiverIn order to reduce surface temperatures passively we

have considered, a multi-pass receiver. The receiver is made

Fig. 13. Mass flow rates required for equal exit temperatures.

Fig. 14. Surface temperatures using eleven pipe diameters. Fig. 15. Surface temperatures for a dual-pass receiver.

N. Boerema et al. / Solar Energy 97 (2013) 356–368 365

of pipes all with the same diameter, with the fluid first pass-ing through a quarter of the tubes on each side of the recei-ver. The fluid is then combined in a header before passingthrough the remaining tubes. The results for the surfacetemperatures can be seen in Fig. 15. The results show amaximum surface temperature of 695 �C with the firstheader temperature of 307 �C.

The efficiency for this receiver under the modelled con-ditions is 92.0%, a 0.8% efficiency increase compared tothe single diameter receiver. As with the multi-diameterreceiver, this small increase in efficiency is due to thedecrease in area with high temperatures for a relativelysmall increase in the maximum temperatures.

3.2. Off-centred flux distribution

To examine the effect of the focus point of the mirrorsdrifting away from the centre of the receiver, surface tem-peratures have been modelled using a mean focus point50% of the distance between the centre and the side edge

of the receiver. Surfaces temperatures for the single diame-ter receiver can be seen in Fig. 16, which shows a maximumtemperature of 943 �C if control for ensuring a minimumflow rate is not used.

To investigate the effect of off centre focusing on themulti-diameter design, we have applied the same distribu-tion as for Fig. 16. For this particular receiver design, itcan be seen that very high surface temperatures will resultif the aiming point for all of the heliostats moves awayfrom the centre of the receiver and an outlet temperatureof 570 �C is still maintained (Fig. 17). The resultant maxi-mum temperature under these conditions (1361 �C) is418 �C above a single diameter design and would likelycause damage to the receiver. As detailed, control methodsare possible to ensure that these situations do not occur,however, the increased risk of catastrophic failure mustbe considered in deciding the best receiver for a particularapplication.

The effect of focus drift on surface temperatures for themulti-pass receiver can be seen in Fig. 18. The maximum

Fig. 16. Surface temperatures for a single diameter receiver with aimingpoint 50% of the distance between the centre and the side edge of thereceiver.

Fig. 17. Surface temperatures for a multi diameter receiver with aimingpoint 50% of the distance between the centre and the side edge of thereceiver.

Fig. 18. Surface temperatures – with aiming point 50% of the distancebetween the centre and the side edge of the receiver.

Fig. 19. Table top flux distribution across the aperture of the multi-passreceiver. Stepping in irradiance from 0.5 MW/m2 to 1 MW/m2 for thecentral 2/3 of the receiver. Vertical lines represent the edge between firstand second pass.

Fig. 20. Surface temperatures for a multi-pass receiver using a table topflux distribution. The outside headers each contain 15 tubes (1/4 of thereceiver).

366 N. Boerema et al. / Solar Energy 97 (2013) 356–368

temperature is 789 �C which is about 570 �C lower thanusing the multi-diameter design and 154 �C below the sin-gle-diameter design. This demonstrates the lower risk ofthis design to incidents of high surface temperatures undernormally distributed flux intensities.

3.3. Alternative flux distribution

Whilst the predominant flux distribution on a billboardreceiver will, in general, be similar to a bell curve distribu-tion (Vant-Hull, 1984; Schiel and Geyer, 1988; Ballestrınand Monterreal, 2004), the occurrence of alterations to thisdistribution may occur. One distribution may be where theirradiance steps up considerably for the main portion of the

Table 3Summary of results for the different billboard receiver concepts.

Receiver concept Efficiency (%) Centre aim point 0.75�Width aim point Thermal expansion difference (mm)

Maximum surface temperature (�C)

Single diameter 91.2 861 943 8.3Ideal flow 91.6 634 n/a 1.5Even flux 91.8 632 n/a 0Multi-diameter 92.6 707 1361 5.9Multi-pass 92.0 695 789 2.6

N. Boerema et al. / Solar Energy 97 (2013) 356–368 367

receiver-leading to a more table-top shaped distribution.This may occur if the heliostats in close proximity to thereceiver, which have a lower variance, were focused usinga uniform aiming point strategy across a portion of thereceiver. This has been modelled for the multi-pass receiverusing an idealised table-top flux distribution that stepsfrom 0.5 MW/m2 to 1 MW/m2 for the central two-thirdsof the receiver. Whilst this is an idealised case, the aim isto achieve an understanding of the influences of a table-top flux distribution (see Figs. 19 and 20).

The result is that as the step in irradiance does not occurbetween the tubes on the edges of the headers, higher tem-peratures occur for some of the tubes. However, whenlooking at the average surface temperatures of the tubesfor the outer headers the maximum difference is 84.4 �Cwhich equates to a difference in length from thermal expan-sion of just over 2 mm.

4. Conclusion

Resultant surface temperatures for four different tubularbillboard designs have been presented. The effect of eachdesign under off-centre focus of the heliostat field andunder a table-top flux intensity distribution has also beenexamined. The high variation in HTF outlet temperaturesfor the single-diameter receiver resulted in high surfacetemperatures, with a maximum of 861 �C. The ideal flowreceiver can reduce surface temperatures however a costeffective method to achieve this must be demonstrated.The multi-diameter receiver partially reduced surface tem-peratures; however, it increased the risk of possible hightemperature events. Surface temperatures above 1300 �Cresulted when the focus point was shifted away from thereceivers centre while trying to maintain a constant receiverheader outlet temperature. The multi-panel receiver, whilehaving greater design complexity, was shown to bothreduce surface temperatures and reduce the impact ofnon-standard irradiation conditions. Under a table-top dis-tribution, this receiver design also maintained compara-tively low maximum surface temperatures. An increase inthe temperature differences between tubes connected tothe same header was apparent; however, these differencesare still considerably lower compared to those on the singlediameter receiver under a standard flux distribution. As themaximum stress, corrosion rates and crack propagation

will all be reduced with a reduction in surface temperatures,and as the number of cycles to failure is increased with areduction in the maximum stress this modelling demon-strates the potential improvement that can be achievedthrough using optimised receiver designs, where the cost/benefit must be analysed. Furthermore, the surface temper-ature distributions and maximum temperatures will assistin receiver material selection to achieve the design lifetime.The maximum surface temperatures for both on and offdesign positioning of the flux aim point, along with receiverefficiencies and the differences in thermal expansion calcu-lated using pipe average temperatures are summarised forthe discussed receiver concepts in Table 3 below.

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